Question

Two objects having masses in the ratio 3 : 4 have the same magnitude of momentum. Their kinetic energies must be in the ratio

• A. $\frac{3}{2}$
• B. $\frac{2}{3}$
• C. $\frac{4}{3}$
• D. $\frac{3}{4}$

Answer 1

The correct option is C $\frac{4}{3}$

$K.E.=\frac{P^2}{2m}K.E{.}_1=\frac{P^2}{2m_1},K.E{.}_2=\frac{P^2}{2m_2}K.E{.}_1\text{is the kinetic energy of}\text{first object}K.E{.}_2\text{is the kinetic energy of}\text{second object}\text{Taking the ratio we get}\frac{K.E{.}_1}{K.E{.}_2}=\frac{\frac{P^2}{2m_1}}{\frac{P^2}{2m_2}}=\frac{P^2}{2m_1}\times \frac{2m_2}{P^2}\frac{K.E{.}_1}{K.E{.}_2}=\frac{m_2}{m_1}=\frac{4}{3}$